My goal is to price various derivatives resetting to 1M and 3M LIBOR via using a lattice. I have calculated an OIS curve for discounting and adjusted 1M and 3M LIBOR forward curves to be consistent with OIS discounting and current LIBOR/basis swap rates.
Is there a way to go about doing this (with possibly some simplifying assumptions) with a short rate model (Hull-White in this case) which has:
- Analytical formulas for caplet and swaption prices for the calibration step.
- Only requires a 1 parameter short rate lattice to be built for derivative pricing (of say Bermudan swaptions of some sort).
I'd be happy to get some reference(s) for formulas in (1), and perhaps some advice on (2). I'm wondering if there is a way to use market vols to produce a short rate lattice implying the correct forward rates for setting up the cash flow, then build another short rate lattice for discounting via adjusting the first lattice uniformly downward at each tenor to match the OIS discount curve. Any ideas on how one could attack this would be helpful!